The previous two chapters are concerned with the elastic behaviour of composites containing fibres which are, in effect, infinitely long. The preparation of composites containing short fibres (or equiaxed particles) allows scope for using a wider range of reinforcements and more versatile processing and forming routes (see Chapter 11). Thus, there is interest in understanding the distribution of stresses within such a composite, and the consequences of this for the stiffness and other mechanical properties. In this chapter, brief outlines are given of two analytical approaches to this problem. In the shear lag model, a cylindrical shape of reinforcements is assumed, and the stress fields in fibre and matrix are simplified so as to allow derivation of straightforward analytical expressions for the composite stiffness. The Eshelby method, on the other hand, is based on the assumption that the reinforcement has an ellipsoidal shape (which could range from a sphere to a cylinder or a plate). This allows derivation of an analytical solution which is more rigorous than that of the shear lag model, but with the penalty of greater mathematical complexity. In the treatment given here, attention is concentrated on the principle of the Eshelby approach; sources are suggested for readers needing more mathematical details.